approved for public release - federation of american ... · determinations of the number of nuclei...

APPROVED FOR PUBLIC RELEASE


Report written:October 15, 1.954

Work done by:——R. B. 13eysterL. CranbergR. B. DayR. L. lienkelR. L. MillsR. A. NoblesT. R. RobertsR. K. SmithS. G. SydoriakR. G. TaylorM. Walt

... . . . ......-

~–

UNCLA$ISIFIED\<

LOS ALAMOS SCIENTIFIC LABORATORY

of the

UNIVERSITY OF CALIFORNIA

._ .

LA-1853 This document consists of& p~es -,:

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.-

-. LTOTAL NEUTRON CROSS SECTION OF He3

. .-

PHYSICS AND MATHEMA TICS(M-3679, 15th edition)

mnni



ABOUT THIS REPORT

This official electronic version was created by scanning the best available paper or microfiche copy of the original report at a 300 dpi resolution. Original color illustrations appear as black and white images. For additional information or comments, contact: Library Without Walls Project Los Alamos National Laboratory Research Library Los Alamos, NM 87544 Phone: (505)667-4448 E-mail: [email protected]

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UNCLASSIFIED

LA-1653

1-20212223242526-30313233-3536373839-41424344-4546-515253545556575859-61626364-676869-7677-7879608182-858687-8889909192-939495969’7.99100101102103104-107108109110111112113114115116-118119-121122-123124125126-129130131-145

WICLASSIFIED



ABSTRACT

The total neutron cross section of He3 has been measured over the

energy range from 200 kev to 22 Mev in good geometry. The main feature

of the curve is a maximum at 2 Mev, superimposed on a decrease in cross

section that is otherwise monotonic with increase in energy. Where the

known He3(n, p)T cross section overlaps these measurements, it comprises

about one-third of the total cross section and has a similar variation with

energy. The total elastic scattering cross section is obtained from the

difference bel.ween the total cross section and the (n, p ) cross section for

neutron energies from 600 kev to 4 Mev.I

-3--.—.

——



UNCLASSIFIED

1. Introduction

Elecause of3

with He can be

the very strong bhdlng of the last nucleon

interpreted in terms of the characteristics

4in He , the interaction of neutrons

of the alpha particle at high ex-

citatiorm, i. e. , from about 20.5 Mev to about 35 Mev for the range of these measurements.

‘I’he compound states formed by the scattering of neutrons from He3 3and H are two mem-

bers oi an isotopic spin triplet, with T ~ . 0 and Tz = +1, respectively. The third, with

T ~ = -1, corresponds to protons incident on He3, or excited states of Li4. It should be of

interest to compare the properties of the members of this triplet because of their bearing on

the charge independence of nuclear forces. This triplet has the unique property that in ad-

dition to the substitution of an n-n for p-p bond (the property of mirror nuclei), there is one

n-p bond substituted for one n-n or p-p bond. The total scattering cross section is obtained

from the difference between the total cross section and what is known of the total reaction

cross section. No direct measurements of the elastic scattering of neutrons from He3 have

been reported as yet.

These measurements may be regarded as part of an informal program of fundamental

nuclear measurements of the very light nuclides

hers of the Los Alamos Scientific Laboratory in

cilitated by access to large quantities of H3 and

which have been carried out by various mem-

recent years, a program which has been fa-

He3.

2. Method and Procedure

The total cross section of He3 for monoenergetic neutrons has been calculated from the

results of a measurement in good geometry of the neutron transmission T of a vessel filled

with He3, according to the

where N is the number of

section to be determined.

formula

He3 nuclei per

The vessel. was cylindrical, 1 meter

T . e-No

square centimeter of sample, and u is the cross

long, 7/8 inch i. d., with a l/16-inch wall, welded

end-cups 0.100 inch thick, a filling line of flexible capillary tubing, and double valves, all of

stainless steel. A detailed description of the design and testing of the vessel is to be found1in a report by R. L. Mills and F. Edeskuty. This cell was used earlier for the measure-

2ments of the total neutron cross section of tritium.

FUling of the vessel and subsequent recovery of the He3 were carried out by T. R.

Roberts. An account of this work is given in Appendix A.



Determinations of the number of nuclei per square centimeter of the sample were car-

ried cut by PVT measurements and by weighing, together with a mass-spectroscopic analysis

of the sample. This work was done by Roberts and Mills. A report by Mills describing the

work is given in Appendix B. The filling pressure was 1450 psi, corresponding to 1.47 moles

of He:]. The impurities were less than 0.4 per cent of the number of He3 moles.

Monoenergetic neutrons were generated by the large Van de Graaff, using the reaction

T(p, n)He3 for the neutron energy range from 0.14 to 4.25 Mev. For the range from 4.25 to

8.03 Mev the reaction J3(D, n) Hea was used, and for the range from 14.2 to 21.4 the reaction

was T(D, n) He4. Tn all cases gas targets were used, sealed off with l/20-mil nickel foil.

The target-to-detector distance was 152 cm, with the gas vessel midway between them.

The detector was a stil,bene scintillator, 3/4 inch in diameter and 1 1/2 inches long, coupled

to a Dumont 6467 photomultiplier, which was followed by a linear amplifier and scaler. The

same detector system was used for all the data; only the amplifier gain, photomultiplier volt-

age, and scaler bias were changed with energy.

:Backgrounds were taken with a copper bar 24 inches long in place of the cell, and with

the target evacuated. The amplifier gain and scaler bias were set so that the counting rate

with the copper bar in place was 1 per cent or less of the counting rate without the

flux with sample out was taken with a dummy evacuated cell in lieu of the sample.

Sufficient counts were taken to assure an over-all rms error of not more than

in the transmission.

3. Results

bar. The

1 per cent

The cross sect ions obtained as a function of energy are summarized in Table 1, in curve

1 of Fig. 1 on a log-log scale, and in Fig. 2 on a linear scale. The neutron energies given

correspond to the average energy of a neutron generated in the gas target. The spread in

neutron energy given in

thickness of the target.

tron energy, except for

tector and the shape of

Table 1 is due to the target thickness and corresponds to half the

This spread is to be interpreted as half the effective spread in neu-

the two lowest energy points. At those energies the bias of the de-

the yield curve discriminated against the lower-energy neutrons, so

that the spread in effective energy is less than the spread in neutron energy, perhaps only

two-thirds as much.

The observed transmissions range from 0.44 to 0.83. The uncertainty in the cross

section associated with the 1 per cent standard error of the transmission, which is due to

statistical uncertainty, is 2 per cent for the lowest transmission and 5 per cent for the highest.

Other sources of uncertainty in the cross-section including effect of He3 impurities, uncertainty



TABLE 1

TOTAL NEUTRON CROSS SECTION OF He3 AS A FUNCTION OF ENERGY

En,

Mev

0.14

0.28

0.39

0.505

0.’736

0.955

1.17

1.39

1.60

1.77

2.02

2.22

2.42

2.63

2.83

3.04

3.23

3.44

3.64

3.84

4.05

A,En,

Mev

*CI.050

+0.040

*0.050

*0.047

+0.042

*0.038

*0.035

*0.032

+0 .030

*0.027

*0.025

&O.023

*0.021

*0.021

*0.020

+0.019

*0.019

*0.018

+0.018

*0.018

*0.017

at’barns

3.44

3.12

2.92

2.82

2.75

2.85

2.95

3.09

3.20

3.20

3.23

3.28

3.08

3.06

2.97

2.95

2.85

2.86

2.74

2.66

2.57

-6-

En,

Mev

4.25

4.85

5.44

5.97

6.50

7.00

7.52

8.03

14.8

16.0

16.9

17.6

18.2

18.8

19.3

19.9

20.4

20.9

21.4

AEn,

Mev

+0.016

*O.1OO

*0.075

+0.063

*0.057

*0.052

*0.046

*0.035

*0.250

*0.400

*0.200

*0.120

+0.090

*0.075

*0.060

*0.055

*0.050

ko.045

*00040

at’

barns

2.58

2.40

2.28

2.19

2.04

2.01

1.90

1.86

1.14

1.04

1.02

0.96

0.88

0.93

0.88

0.87

0.87

0.88

0.81



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— APPROVED FOR PUBLIC RELEASE


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in the dimensions and contents of the cell, and inscattering by the sample, are estimated to

have a combined effect not greater than 1 per cent at any cross section. The sum of the

statistical and miscellaneous uncertainties at each energy is very close to 0.06 barns.

The most noteworthy feature of the results is the broad maximum centered at 1.9 + 0.2

Mev, superimposed on a decrease that is monotonic with increasing energy. The general shape

is similar to that which has been found by Coon et al.2 for the total cross section of tritium,

that is, a broad maximum in the Mev region, followed by a smooth drop at higher energies.

At low energies the He3 cross section increases, presumably because of the large He3(n, p )T

contribution to the cross section at the lower energies.

hi the region up to 4.35 Mev neutron energy, the only reactions of neutrons with He3

energetically possible are elastic scattering, radiative capture, and the (n, p ) reaction. If,

following Flowers and Mandl,3 it is assumed that the cross section for He3(n, y)He4 is of the

same order of magnitude as T(p, y)He4, that is, of the order of 10-28 cm2, then the difference

between the total neutron cross section and the (n, p ) reaction cross section is essentially the

elastic scattering cross section.

Curve 2 in Fig. 1 is an extrapolation on a I/v basis of the total cross section for He3

from measurements at thermal and subthermal energies by King and Goldstein.4 This extra-

polation provides a rough estimate of that part of the total cross section due to the (n, p ) re-

action. A more reliable estimate of the latter can be obtained from the principle of detailed

balance by using the results of Jarvis et al.5 and Willard et al.6 for the inverse reaction

T(p, n)He3. These are given as curves 3 and 4, respectively, of Fig. 1. In the case of

Willards data, only that part of the results which corresponds to the experimental points is

used. ‘The extrapolation to threshold is presumed in error because it does not have the cor-

rect slcjpe at threshold and corresponds to a decrease in the (n, p ) reaction cross section with

decrease in energy. A lhird set of data taken at this Laboratory with improved background

determinations corroborate Willards’s results.6 The discrepancy between Jarvis et al. and

Willard et al. is therefore to be resolved in favor of the latter. Direct data on the reaction8cross section obtained by Coon are consistent with the data of curves 3 or 4.

.The difference between the total neutron and the Hes (n, p ) T cross sections is given in

Fig. 3, curve 1, using Willard’s data. For comparison, curve 2 of Fig. 3 gives the curve of

total neutron cross section for tritium as measured by Coon, Bondelid, and Phillips.2 This

is reasonably certain to be entirely due to elastic scattering up to the threshold

8.34 Mev.

At 4.36 Mev, the reaction lIe3(n, D )D becomes possible.

Keyser$t on the inverse reaction, and the principle of detailed

From the data of

balance, the (n, d)

for T(n, 2n)D,

McNeil and

reaction

-9-



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‘T-

LIf0

i’

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accounts for 0.004 barn at a neutron energy of 4.50 Mev. From Hunter and Richards10

data

and detailed balance, the (n, d) reaction accounts for 0.097 barn at 6.4 Mev neutron energy,

or about 5 per cent of the total. It seems likely that above 4.35 Mev the (n, p ) reaction con-

tinues to account for an appreciably larger percentage of the total cross section than this, so

that further data on the He3(n, p )T reaction are necessary to extend knowledge of the elastic

cross section.

It is noteworthy that the reaction and total cross sections have maxima at the same

energy, within experimental error, and, have similar general shapes down to 400 kev. Their

ratio varies smoothly from 0.38 to 0.22, with increasing energy. It is interesting, too, to3 3

note that the peak cross sections for elastic scattering of neutrons from H and He are

equal within the over-all uncertainty of about 0.1 barn. The energies at which the maxima

occur differ by about 2 Mev.

4. Discussion

at 2 Mev may be interpreted

resonance of about 2.6 barns,

interpretation has been placed

The only theoretical interpretation of these data made thus far is by J. Gammel. He

has suggested, tentatively, that the maximum in the scattering

as a p-wave resonance with J = 2. This gives a maximum at

compared to the experimental value of 2.45 barns. The same

on the maximum of the tritium results.

The results on the elastic scattering are of interest in comection with the frequently

made suggestion that the He3(n, p )T reaction be used as a neutron spectrometer. 11The chief

source of background in such an instrument arises from elastic scattering, and these data pro-

vide a basis for estimating quantitatively the importance of this background.

I

I

-11- .

I

I



----—. ....-

APPENDIX A

He3 CELL FILLING AND RECOVERY

By T. Roberts

The gas vessel was filled with He3, using a modification of the cryogenic pump technique

described by Mills and Edeskutyl in connection with the tritium filling of the same vessel.

The main difference was that the He3 was supplied in 12-liter cans at an average pressure

of about 400 mm Hg instead of uranium pots. In order to condense most of the He3 into the

pump, the surrounding He4 bath was cooled by pumping to about 1.2°K, at which temperature

the vapor pressure of He3 is about 20 mm.

The high-pressure filling line and glass vacuum line were similar to those shown in

Figs. ~, and 7 of Mills nnd Edeskuty, 1 which are reported here as Figs. 4 and 5. The pres-

sure gauge was a Heise O to 5000 psi gauge filled with mercury to reduce dead volume. A

diffusion pump was comected to the high-pressure gauge manifold by only one autoclave valve

in order to increase the pumping speed. The nine He3 tanks furnished by LASL Group CMR -4

were interconnected by a low-pressure manifold of l/8-inch copper tubing and were also con-

nected to the main manifold by a high-pressure valve.

The cryogenic pump was designed to withstand 86001;!

tions. The pump had a volume of 87 cc and was made

piece of 2 l/2-inch round 321-stainless steel stock. The

psi, according to ASME specifica-

by drilling a 1 l/2-inch hole in a

plug had 1 3/4 standard fine threads.

High-pressure tubing 1/4 inch o.d., 3/32 inch id. , was used for the pump inlet tube to pre-

vent the likelihood of air or tritium plugs. In order to warm the cryogenic pump to room

temperature quickly, a l.00-watt wire-wound resistor was taped to the pump.

The pump was pressure tested for 16 hours at 8600 psi and the pump, gauge, and high-

-pressure cell were tested for 60 hours at 1800 psi. To the limit of detectability, about

0.3 per cent, there was no loss in pressure in either experiment.

The only difficulties encountered concerned the sticking of valves on two He3 tanks. It

had been hoped, on the basis of labeled tank contents, that the cell could be filled to 1500 psi

or more, but one tank u’as found to be empty, apparently because the valve stuck shut during

the filling by Group CMR -4. The valve on another tank failed to open during the condensation,

so that 1452 psi at a cell temperature of 28.5°C, was the maximum pressure that could be

achieved.

The He4 dewar contained about 5 1/2 liters, 3 1/2 of which were used up in pumping

the He<Lbath down to 1.2°K and in condensing the He3. Condensation was stopped when the

storage-can pressure had fallen to 55 mm.

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The empty He3 tank was useful in the recovery operation. After the cell filling, the

cryogenic pump and high-pressure manifold were bled down to 14 mm pressure by a two-stage

expansion, first, into two of the tanks whose pressure was 55 mm, and then into the empty

tank. The high-pressure manifold was then emptied with the Toepler pump.

After the cross-section measurements, the cell was reconnected to the high-pressure

manifold and the pressure measured as 1441 psi at 27.9°C. The pressure drop was completely

accounted for by the temperature change and the expansion into the empty manifold. The cell

was then emptied to 500 mm pressure by expansion into seven of the tanks and a sample

taken for mass spectrometer analysis. The cell contents then were expanded into the nearly

empty tank to 32 mm and the remaining gas removed by Toeplering for three days.

-15-.—..—.,. .~-——_ .__ .._.. .._-c ...-4

#



APPENDIX B

He3 CELL CONTENT

By R. L. Mills

The total charge in the cell was computed by PVT relationships as indicated in Table 1

and from weight changes as shown in Table 2. Results of the mass-spectrographic analysis

of the gas sample are entered in Table 3.

TABLE 1

CELL CONTENT AS DETERMINED BY PVT

Pressure, Volume, Temperature, Cell Content,atm cc oK moles

98.80 * 0.10 384.220 * 0.077 301.6 + 0.1 L468(a)

1.470(b)

1.468(C)

1.470(d)

average 1.469 + 0.002

(a)Co reputed from the virial equation

pv = RT [1 + B(T)/v]

using a value for B(T) determined from the equation

B = (l{T) 1/4 [16.4873 - 74.09( 1/T) ’/2 - 24.6(1/T)] cc/g

as given by F. G. Keys, Temperature, pp. 45-59, Reinhold Publishing Corporation, New York,

1941.

(b)Computed from the virial equation using for B(T) the value 11.38 cc/mole, interpolated

from data rep,orted by W. H. Keesom, Helium, Table 205, p. 38, Elsevier Publishing Company,

Amsterdam, 1942.

(c)Computed from A. C. Johnson’s equation of state

PV = 24875.08 + 11.802p - 0.()() 1094pz cc atm/mole at KIOC

and corrected to 28.5° C. See “IV - Vapor Pressure, Specific Volume, PVT Data for H2, N2,

02, CO, C02, Air, He, A, Hg,” by S. Gratch, Trans. ASME, ‘Q 635 (1948).

(d)Computed from an interpolation of data reported by R. Weibe, V. L. Gaddy, and Conrad

Heins, Jr., “The Compressibility Isotherms of He from -70 to 200° and at Pressures up to

1000 atm,” J. Am. Chem. Sot., 53, 1721 (1931).

-16-

.. . .

-—. :-. J



—.

CELL

Wt. Cell FullMinus Tare, g

4.476

TABLE 2

CONTENT AS DETERMINED BY WEIGHT DIFFERENCE OF CELL

Wt. Cell EmptyMinus Tare, g

0.017

—(a) Based on an “average molecular weight”the mass-spectrographic data of Table 3.

Wt. of Gasin Cell, g

4.459 * 0.005

of 3.0685 for the gas

‘b ‘Assuming pure He3 with molecular weight 3.0170.

TABLE 3

MASS SPECTROGRAPHIC ANALYSIS

Symbol Mass h’umber

He3 3

‘228

‘22

HT 4

‘2 6

HD 3

DT 5

Computed. cell contents in Tables 1 and 2 do not

OF CELL

Cell Content,moles

1.453 * o.oo2(a)

1.478 + 0.002(b)

mixture, as computed from

SAMPLE

Mole %

99.62

0.20

0.05

0.05

0.04

0.02

0.02

agree within the combined experimental

errors. Such a discrepancy could easily arise if the gas sample analyzed in Table 3 was not

truly representative of the cell content. For this reason the results of Table 1 have been used

to compute the following concentrations, where L, the cell length, is 99.981 + 0.005 cm, and

N, Avogadro’s number,23

is taken as 6.0228 + 0.0011 x 10 :

(n/V)

(L) (n/V)

(N)(L) (n/V)

(0.9962 )(N)(L) (n/V)

(0.0020 )(N)(L) (n/V)

= 0.003823 * 0.000005 mole/cc

= 0.3822 * 0.0005

= 2.302 * 0.003 X

= 2.293 * 0.003 X

= 0.0046 X 1023

2mole/cm

~023molecules/cm2

~023molecules He3/cm

2

molecules N2/cm2

-17-—_L-—---- __

. ...-. . . . ~... -”



1. R. L. Mills and I?. Edeskuty,

2. J. H. Coon, R. Bondelid, and

3. B. H. Flowers and F. Mandl,

References

LAMS-141 1, August 1952 (not available).

D. Phillips, LA-1483, November 1952.

Proc. Roy. Sot. London, A206, 131 (1951).

4. L. D. P. King and L. Goldstein, Phys. Rev., 73, 1366 (1949).

5. ,Jarvis, Hemmendinger, Argo, and Taschek, Phys. Rev., ‘@ 929 (1950).

6. H. B. Willard, J. K. Bair, and J. D. Kington, Phys. Rev., 9A, 865 (1953).

7. IG. A. Jarvis, private communication.

8. J. H. Coon, Phys. Rev., 80, 488 (1950).

9. ‘K. G. McNeil and G. M. Keyser, Phys. Rev., 8Q, 602 (1951).

10. IG. T. Hunter and H. T. Richards, Phys. Rev., ~, 1445 (1945).

11. ;R. Batchelor, Proc. Phys. Sot. London, A65, 674 (1952).

12. “Unfired Pressure Vessels, Section VII I, ASME Boiler and Pressure Code, 1952.

-18-

.— -_ .-.-.

~“



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